Abstract

The equivalents of the classical theorems of hydrodynamic stability are derived for inviscid flow through a flexible tube. Both axisymmetric and non-axisymmetric perturbations in flows in cylindrical geometries are analyzed. For the practically important case of Hagen-Poiseuille flow, the present analysis indicates that axisymmetric perturbations are always stable, while highly non-axisymmetric perturbations could be unstable. This is in contrast to plane parallel flows where two-dimensional disturbances are always more unstable than three-dimensional ones.